Data compiled from a variety of sources follow Benford’s law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benford’s law. Finally, three chaotic systems are considered: Lorenz, Hénon, and Rössler. The Lorenz system generates trajectories that follow Benford’s law. The Hénon system generates trajectories that resemble neither the uniform distribution nor Benford’s law. Finally, the Rössler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford’s law for others.
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June 2000
Research Article|
June 01 2000
Do dynamical systems follow Benford’s law?
Charles R. Tolle;
Charles R. Tolle
Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415-2208
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Joanne L. Budzien;
Joanne L. Budzien
Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415-2208
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Randall A. LaViolette
Randall A. LaViolette
Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415-2208
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Chaos 10, 331–336 (2000)
Article history
Received:
November 23 1999
Accepted:
March 14 2000
Citation
Charles R. Tolle, Joanne L. Budzien, Randall A. LaViolette; Do dynamical systems follow Benford’s law?. Chaos 1 June 2000; 10 (2): 331–336. https://doi.org/10.1063/1.166498
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